Find the difference between simple interest and true discount on Rs. 960 due 4 year hence at `5%` per annum simple interest-

Options

A. Rs. 32
B. Rs. 52
C. Rs. 42
D. None of these

Answer

To solve the problem of finding the difference between simple interest (SI) and true discount (TD) on Rs. 960 due in 4 years at a rate of 5% per annum, we can follow these steps:

### Step 1: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 960 \) (Principal)
- \( R = 5 \) (Rate of interest)
- \( T = 4 \) (Time in years)

Substituting the values:
\[ SI = \frac{960 \times 5 \times 4}{100} \]
Calculating the multiplication:
\[ SI = \frac{960 \times 20}{100} \]
\[ SI = \frac{19200}{100} = 192 \]

### Step 2: Calculate the True Discount (TD)
The formula for True Discount is:
\[ TD = \frac{SI}{1 + \frac{R \times T}{100}} \]
First, we need to calculate \( 1 + \frac{R \times T}{100} \):
\[ 1 + \frac{5 \times 4}{100} = 1 + \frac{20}{100} = 1 + 0.2 = 1.2 \]
Now substituting the values into the TD formula:
\[ TD = \frac{192}{1.2} \]
Calculating the division:
\[ TD = 160 \]

### Step 3: Find the Difference between SI and TD
Now we can find the difference:
\[ \text{Difference} = SI - TD = 192 - 160 = 32 \]

### Final Answer
The difference between the Simple Interest and True Discount is Rs. 32.

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